Gravitational-Wave Constraints on $R^2$ Gravity

Abstract

Gravitational waves from compact binary coalescences provide a unique opportunity to test general relativity in the strong-field regime. Quadratic $f(R)=R+aR^2$ gravity is among the simplest higher-curvature extensions of general relativity and introduces a massive scalar degree of freedom whose finite interaction range can modify compact-binary dynamics and gravitational-wave emission. We map this theory onto the effective-field-theory waveform for generic massive scalar-tensor gravity, obtaining a theory-specific inspiral phase correction governed by the single coupling parameter $a$. Using Bayesian analyses of the binary-neutron-star events GW170817 and GW190425, we obtain a combined constraint on the quadratic-curvature coupling of $a\lesssim6.2\times10^6\,\mathrm{m}^2$ at $90\%$ credibility, corresponding to a lower bound on the scalar mass of $m_s\gtrsim3.2\times10^{-11}\,\mathrm{eV}$. This constitutes the strongest astrophysical constraint on the quadratic-curvature coupling, improving the previous best bound by approximately five orders of magnitude and demonstrating the sensitivity of binary-neutron-star inspirals to finite-range scalar interactions in the strong-field regime.